Non-Equilibrium Dynamics Beyond Dephasing: Recurrences and Loss Induced Cooling in One-dimensional Bose Gases PDF
Preview Non-Equilibrium Dynamics Beyond Dephasing: Recurrences and Loss Induced Cooling in One-dimensional Bose Gases
Springer Theses Recognizing Outstanding Ph.D. Research Bernhard Rauer Non-Equilibrium Dynamics Beyond Dephasing Recurrences and Loss Induced Cooling in One-dimensional Bose Gases Springer Theses Recognizing Outstanding Ph.D. Research Aims and Scope The series “Springer Theses” brings together a selection of the very best Ph.D. theses from around the world and across the physical sciences. Nominated and endorsed by two recognized specialists, each published volume has been selected foritsscientificexcellenceandthehighimpactofitscontentsforthepertinentfield of research. For greater accessibility to non-specialists, the published versions includeanextendedintroduction,aswellasaforewordbythestudent’ssupervisor explainingthespecialrelevanceoftheworkforthefield.Asawhole,theserieswill provide a valuable resource both for newcomers to the research fields described, and for other scientists seeking detailed background information on special questions. 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More information about this series at http://www.springer.com/series/8790 Bernhard Rauer Non-Equilibrium Dynamics Beyond Dephasing Recurrences and Loss Induced Cooling in One-dimensional Bose Gases Doctoral Thesis accepted by the Atominstitut, TU Vienna, Vienna, Austria 123 Author Supervisor Dr. Bernhard Rauer Prof. Hannes-Jörg Schmiedmayer Laboratoire Kastler Brossel Atominstitut ÉcoleNormale Supérieure TU Vienna Paris, France Vienna,Austria ISSN 2190-5053 ISSN 2190-5061 (electronic) SpringerTheses ISBN978-3-030-18235-9 ISBN978-3-030-18236-6 (eBook) https://doi.org/10.1007/978-3-030-18236-6 ©SpringerNatureSwitzerlandAG2019 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped. 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Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland ’ Supervisor s Foreword Thequestionofwhetheranisolatedquantummany-bodysystemrelaxesisacentral problem at the interface between microscopic quantum dynamics and statistical physics.Itisofhighrelevanceinmanydiversefields,rangingfromdecoherencein quantum information and metrology to the complex dynamics in high-energy physicsandcosmology.Moreover,relaxationprocessesareintimatelyrelatedtothe question if and how the classical world at the macro-scale can emerge from the unitary quantum evolution at the micro-scale. The thesis of Bernhard Rauer investigates a series of questions that are highly contestedinthiscontext:Howdoesanisolatedquantummany-bodysystemrelax? Towhatextentandthroughwhichprocessesisthememoryofaninitialstateerased during time evolution? How does a classical ensemble description in the sense of statistical physics emerge from the underlying quantum evolution when an actual environment is absent? Over the last years, ultracold gases have emerged as an ideal model system to study these questions. They are nearly perfectly isolated and a large set of tools is available to manipulate and probe their many-body physics in a controlled setting. One-dimensional (1d) gases are especially interesting in that context. They exhibit very rich dynamics and can be compared to well-studied theoretical models. An especiallyinterestingaspectisthatinmany1dsystemsalargenumberofconserved quantities constrain the evolution and have a profound effect on their relaxation processes. In his thesis, Bernhard Rauer investigates relaxation dynamics in degenerate 1d Bose gases of 87Rb atoms, confined on an atom chip. The thesis studies two main topics:thefirstbeingconcernedwiththecreationofthesesystemsinthelaboratory. Inexperimentalrealizations of1dBosegases, thetemperatureofthesystem needs to be brought below the minimal energy of transverse excitations to confine dynamics to the desired single dimension. However, this leads to an exponential suppression of thermalizing collisions which should force thermalization to stop. Nevertheless, evaporative cooling, which highly depends on efficient ther- malizationprocesses,workssurprisinglywellwithinthe1dregimeandexperiments reach temperatures far below the freeze-out of thermalizing collisions. Why these v vi Supervisor’sForeword lowtemperaturescanbereachedremainedamysteryforthelast10years.Bernhard Rauer investigates the cooling process in detail and presents a semi-classical mechanism that describes the cooling as a loss-driven reduction of fluctuations under a continuous dephasing of the involved phononic excitations. This model is ingoodagreementwiththeexperimentalfindingsandfinallyprovidesasolutionto the cooling conundrum. Remarkably, the contribution of atomic shot noise that is expected to become relevant at low temperatures seems to be absent in the measurements. Thesecondfocusofthethesisliesintheout-of-equilibriumdynamicsfollowing a quench. Extending Poincaré’s recurrence theorem to the quantum domain, any finitequantumsystemshouldatsomepointreturnarbitrarilyclosetoitsinitialstate. In large many-body systems, however, the complexity of the many-body eigen- statesandtheirspectrumleadstoexceedinglylongrecurrencetimes.Yet,Bernhard Rauer was able to observe recurrences of coherence in the post-quench relaxation dynamics of a pair of 1d Bose gases. The key to the experiment lies in the insight that one cannot observe the many-body eigenstates directly, but can only observe much simpler few-body observables. These observables can be linked to an effective quantum field theory description through the system’s collective modes. Controllingthedispersionofthesecollectivemodes,inthiscasephonons,allowsto observe recurrences in experimentally accessible quantities. Performing the post-quench relaxation experiments in a box-shaped potential results in commen- surate phonon frequencies such that the observation of their rephasing becomes feasible,evenforsystemsofthousandsofparticles.Boththerecurrencetimeandits scaling with the size of the system are well described by a low-energy Luttinger liquid model. In contrast, the measured damping of the recurrence signal stems mainly from phonon-phonon scattering processes mediated by terms beyond the low-energy effective field theory description. The presented experiment sets a beautiful example of how rephasing can be used to probe many-body processes at times beyond the initial dephasing dynamics, opening up a new window to study quasi-particle interactions in such systems. Another remarkable feature of the experiment is that, even though the system apparently relaxes to a classical (gen- eralized) Gibbs ensemble, coherence underneath this classical statistical physics cover leads to a return of the initial state at the point of the recurrence. This illustrates the intricate connection between the unitary evolution in quantum many-body systems and the description of their relaxed state in terms of statistical mechanics. Vienna, Austria Prof. Dr. Hannes-Jörg Schmiedmayer March 2019 Abstract Out-of-equilibrium dynamics in complex quantum many-body systems is a vast topicofresearchtouchingmanydifferentareasofphysics.Oneofthemostversatile experimental platforms to investigate these effects are ultracold atoms, due to their flexibility and easy isolation from the environment. In this thesis, we investigate non-equilibrium dynamics of one-dimensional (1d) Bose gases realized with ultracold 87Rb atoms on an atom chip. Focusing on phenomena emerging on timescales beyond the typical dephasing times of excitations, we report on the observation of recurrences and the finding of a novel cooling mechanism. Arecurrence,thedynamicreturnofasystemtoitsinitialstate,cangenerallynot be observed in large systems as the complexity of their excitation spectra shifts its appearancetoprohibitivelylongtimes.Yet,byrealizingacommensuratespectrum in a pair of near-homogeneous 1d Bose gases, recurrences in their low-energy dynamics can be observed on experimentally accessible timescales. We demon- strate this by initializing two gases in a phase coherent state by coupling them through a tunneling barrier before suddenly ramping the coupling to zero. The subsequentdynamicsismonitoredbymatter-waveinterferometry,providingaccess to the relative phase field between the gases. After an initial dephasing dynamics, we observe multiple recurrences of the coherent initial state due to a rephasing of the underlying excitations. Additionally, analyzing the damping of these recur- rences, we detect otherwise elusive scattering effects between excitations. Furthermore, we investigate the dynamics of a 1d Bose gas under a continuous loss of particles. With thermalization strongly inhibited in these systems, standard evaporative cooling is rendered ineffective; yet, we still observe a substantial coolingeffect.Thiscoolingisdrivenbyanovelmechanismthatreliesneitheronan energy selective extraction of particles nor on efficient thermalization channels. Instead, it proceeds through a loss-induced reduction of density fluctuations and a continuous dephasing of the involved excitations. For experiments with 1d Bose gases, this mechanism fills an important gap in the understanding of the state preparation and the limits of cooling. vii Acknowledgements I would like to express my gratitude to everybody involved in making this thesis possible,firstandforemostthemembersoftheKRbteam.Coldatomsexperiments canbecomplexbeastsandarebesttamedingroups.Withouttheircountlesshours workingonthemachine,thesharingofcodesandthelongdiscussions,noneofthe results presented here would be possible. Also, I want to thank all current and formermembersoftheAtomchipgroupthatIhadthepleasuretoworkalongwith, for numerous borrowed equipments, stimulating discussions and for creating the most friendly work environment one can wish for. The infamous coffee corner discussions and long evenings will be missed. In particular, I would like to thank the following people: (cid:129) My supervisor Hannes-Jörg Schmiedmayer, for giving me the opportunity to work in his group and for sharing his fascination for physics. (cid:129) Our former team members Micheal Gring, Max Kuhnert, Tim Langen, Remi Geiger, and David Adu Smith from whom I learned a lot and who left us a well-oiled machine. (cid:129) Thomas Schweigler,my mainco-worker on thesetup,for hisrazor-sharp mind always asking the right questions, and for the careful reading of most of this manuscript. Also, for organizing many alpine adventures. (cid:129) Sebastian Erne, Pjotrs Grišins, and Igor Mazets for their theory support, shared codes, and numerous discussions that helped to elucidate the investigated phenomena. (cid:129) ThenextgenerationofKRbteammemberstakingovertheexperiment:Federica Cataldini, Amin Tajik, João Sabino, and SiCong Ji, who will hopefully realize manyinterestingprojectsinthecomingyears.Particularly,Iwouldliketothank Amin for putting all that work into the DMD setup. (cid:129) Jacqueline Bloch for giving me the opportunity to visit her group and learn about the fascinating world of exciton-polaritons. (cid:129) Hanns-ChristophNägerlandIacopoCarusottoforkindlyagreeingtoreviewmy thesis. ix x Acknowledgements (cid:129) The Austrian and European taxpayer for supporting basic research and funding the work presented here. ZuguterLetztmöchteichmeinenFreundenundmeinerFamiliedanken,speziell meinen Eltern für ihre kontinuierliche Unterstützung, die mich zu diesem Punkt gebracht hat. Der größte Dank aber gebührt meiner Partnerin Jaqueline für ihre fortwährende Unterstützung und Motivation, trotz der vielen Abende, die sie ohne mich ver- bringen musste damit dieses Ding hier fertig wird.
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